SOLUTION: The height of a rectangular box is 4 times its width, and its length is 5 ft. more than its width. The volume of the box is 125 ft^3. Find the width of the box. Round your answer t

Algebra ->  Expressions -> SOLUTION: The height of a rectangular box is 4 times its width, and its length is 5 ft. more than its width. The volume of the box is 125 ft^3. Find the width of the box. Round your answer t      Log On


   

Question 832818: The height of a rectangular box is 4 times its width, and its length is 5 ft. more than its width. The volume of the box is 125 ft^3. Find the width of the box. Round your answer to two decimal places.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x for height
y for width
z for length

x=4y, and z=5+y, then volume formula for your box is xyz=%284y%29%2Ay%2A%28y%2B5%29=4y%5E3%2B20y%5E2.

You are given the volume:
4y%5E3%2B20y%5E2=125
highlight%284y%5E3%2B20y%5E2-125=0%29
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Try Rational Roots Theorem with synthetic division to test for roots.
Maybe try a graphing calculator to make this easier.
Not quite to the accuracy you want, but y=2.1 approximately.